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Selection of uncertain differential equations using cross validation

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  • Liu, Z.
  • Yang, Y.

Abstract

Uncertain differential equations have been widely applied to modelling dynamic phenomena with noises. Facing with the same dynamic phenomenon, different scholars may adopt different uncertain differential equations. Naturally, there is a crucial question about which of these equations is most suitable to describe the given dynamic phenomenon. A desired uncertain differential equation should have a good prediction ability, that is, it performs well in a new dataset. As a model selection technique, cross validation assesses the model’s ability to predict new data in order to avoid overfitting. This paper applies k fold cross validation to the selection of uncertain differential equations. Observations in training sets and testing sets are used to calculate generalized moment estimations of unknown parameters and testing errors for uncertain differential equations, respectively. Then the uncertain differential equation with the smallest total testing error is selected. A numerical example and a real data example using closing prices of Industrial and Commercial Bank of China (ICBC) stock illustrate our methods in detail.

Suggested Citation

  • Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921004033
    DOI: 10.1016/j.chaos.2021.111049
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
    2. Lanruo Dai & Zongfei Fu & Zhiyong Huang, 2017. "Option pricing formulas for uncertain financial market based on the exponential Ornstein–Uhlenbeck model," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 597-604, March.
    3. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    4. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    6. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    8. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
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    Cited by:

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    2. Jia, Lifen & Liu, Xueyong, 2021. "Optimal harvesting strategy based on uncertain logistic population model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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